diff --git a/DESCRIPTION b/DESCRIPTION
index 3e878e84bd..00ec8c3bb6 100644
--- a/DESCRIPTION
+++ b/DESCRIPTION
@@ -60,7 +60,8 @@ Authors@R: c(
   person("Jens Peder","Meldgaard", role="ctb"),
   person("Vaclav","Tlapak",        role="ctb"),
   person("Kevin","Ushey",          role="ctb"),
-  person("Dirk","Eddelbuettel",    role="ctb"))
+  person("Dirk","Eddelbuettel",    role="ctb"),
+  person("Ben","Schwen",           role="ctb"))
 Depends: R (>= 3.1.0)
 Imports: methods
 Suggests: bit64 (>= 4.0.0), bit (>= 4.0.4), curl, R.utils, xts, nanotime, zoo (>= 1.8-1), yaml, knitr, rmarkdown
diff --git a/NEWS.md b/NEWS.md
index df1b96436c..3c62f3c261 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -8,6 +8,8 @@
 
 1. If `fread()` discards a single line footer, the warning message which includes the discarded text now displays any non-ASCII characters correctly on Windows, [#4747](https://github.com/Rdatatable/data.table/issues/4747). Thanks to @shrektan for reporting and the PR.
 
+2. `fintersect()` now retains the order of the first argument as reasonably expected, rather than retaining the order of the second argument, [#4716](https://github.com/Rdatatable/data.table/issues/4716). Thanks to Michel Lang for reporting, and Ben Schwen for the PR.
+
 ## NOTES
 
 1. Compiling from source no longer requires `zlib` header files to be available, [#4844](https://github.com/Rdatatable/data.table/pull/4844). The output suggests installing `zlib` headers, and how (e.g. `zlib1g-dev` on Ubuntu) as before, but now proceeds with `gzip` compression disabled in `fwrite`. Upon calling `fwrite(DT, "file.csv.gz")` at runtime, an error message suggests to reinstall `data.table` with `zlib` headers available. This does not apply to users on Windows or Mac who install the pre-compiled binary package from CRAN.
diff --git a/R/setops.R b/R/setops.R
index 1ac949601b..b6dcd7b0b2 100644
--- a/R/setops.R
+++ b/R/setops.R
@@ -62,11 +62,12 @@ fintersect = function(x, y, all=FALSE) {
   if (all) {
     x = shallow(x)[, ".seqn" := rowidv(x)]
     y = shallow(y)[, ".seqn" := rowidv(y)]
-    jn.on = c(".seqn",setdiff(names(x),".seqn"))
-    x[y, .SD, .SDcols=setdiff(names(x),".seqn"), nomatch=NULL, on=jn.on]
+    jn.on = c(".seqn",setdiff(names(y),".seqn"))
+    # fixes #4716 by preserving order of 1st (uses y[x] join) argument instead of 2nd (uses x[y] join) 
+    y[x, .SD, .SDcols=setdiff(names(y),".seqn"), nomatch=NULL, on=jn.on]
   } else {
-    z = funique(y)  # fixes #3034. When .. prefix in i= is implemented (TODO), this can be x[funique(..y), on=, multi=]
-    x[z, nomatch=NULL, on=names(x), mult="first"]
+    z = funique(x)  # fixes #3034. When .. prefix in i= is implemented (TODO), this can be x[funique(..y), on=, multi=]
+    y[z, nomatch=NULL, on=names(y), mult="first"]
   }
 }
 
diff --git a/inst/tests/tests.Rraw b/inst/tests/tests.Rraw
index a6013a3a11..2b44b3038f 100644
--- a/inst/tests/tests.Rraw
+++ b/inst/tests/tests.Rraw
@@ -17258,3 +17258,6 @@ if (identical(x, enc2native(x))) {
   test(2162.2, fread(text = txt2, encoding = 'Latin-1'), out,
                warning="Discarded single-line footer: <<fa\u00e7ile>>")
 }
+
+# fintersect now preserves order of first argument like intersect, #4716
+test(2163, fintersect(data.table(x=c("b", "c", "a")), data.table(x=c("a","c")))$x, c("c", "a"))